On the calibration of the 3/2 model

Abstract

We consider the problem of calibrating the 3/2 stochastic volatility model to option data. In comparison to the characteristic function of the Heston model, the characteristic function of the 3/2 model can be up to 50 times slower to evaluate. This makes the standard least squares calibration with finite-difference gradients unreasonably slow. To address this problem we derive the analytic gradient of the characteristic function in compact form. We then propose a computational method for the analytic gradient formula which caches intermediate results across the partial derivatives, in addition to the strike dimension and the maturity dimension. Compared to the fastest method of calibrating the 3/2 model which we could find in the literature, the method proposed in this paper is more than 10 times faster. We also discuss the issue of apparent non-convexity in the least squares calibration of the 3/2 model for market data. To tackle it, we propose a regularized calibration where the regularization point is obtained using "risk neutral" MCMC estimation of the model. We find that this approach is particularly well suited for the calibration problem as it generates naturally a consistent damping matrix for the parameter estimates, in addition to being very fast.